LMFDB - Embedded newform 672.2.bi.c.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0574700 + 1.73110i) q^{3} +(0.461663 - 0.266541i) q^{5} +(-0.489180 - 2.60014i) q^{7} +(-2.99339 + 0.198972i) q^{9} +O(q^{10})$	\(q+(0.0574700 + 1.73110i) q^{3} +(0.461663 - 0.266541i) q^{5} +(-0.489180 - 2.60014i) q^{7} +(-2.99339 + 0.198972i) q^{9} +(2.28733 - 3.96177i) q^{11} +4.97924 q^{13} +(0.487941 + 0.783866i) q^{15} +(2.16139 - 3.74363i) q^{17} +(0.921087 + 1.59537i) q^{19} +(4.47297 - 0.996248i) q^{21} +(0.103387 - 0.0596907i) q^{23} +(-2.35791 + 4.08402i) q^{25} +(-0.516471 - 5.17042i) q^{27} +7.74542 q^{29} +(1.93668 + 1.11814i) q^{31} +(6.98966 + 3.73191i) q^{33} +(-0.918880 - 1.07000i) q^{35} +(-7.02261 + 4.05451i) q^{37} +(0.286157 + 8.61955i) q^{39} -2.60914 q^{41} +1.87217i q^{43} +(-1.32891 + 0.889722i) q^{45} +(-2.91482 - 5.04861i) q^{47} +(-6.52141 + 2.54387i) q^{49} +(6.60480 + 3.52642i) q^{51} +(2.29287 - 3.97137i) q^{53} -2.43867i q^{55} +(-2.70880 + 1.68618i) q^{57} +(5.71492 + 3.29951i) q^{59} +(-1.07564 - 1.86306i) q^{61} +(1.98166 + 7.68590i) q^{63} +(2.29873 - 1.32717i) q^{65} +(10.4812 + 6.05131i) q^{67} +(0.109272 + 0.175543i) q^{69} -6.20627i q^{71} +(8.35520 + 4.82388i) q^{73} +(-7.20535 - 3.84706i) q^{75} +(-11.4201 - 4.00935i) q^{77} +(0.0228792 + 0.0396280i) q^{79} +(8.92082 - 1.19121i) q^{81} -3.86459i q^{83} -2.30440i q^{85} +(0.445129 + 13.4081i) q^{87} +(-8.23362 - 14.2610i) q^{89} +(-2.43575 - 12.9467i) q^{91} +(-1.82431 + 3.41684i) q^{93} +(0.850463 + 0.491015i) q^{95} -7.18828i q^{97} +(-6.05860 + 12.3143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0574700	+	1.73110i	0.0331803	+	0.999449i
$3$	0.0574700	+	1.73110i	0.0331803	+	0.999449i
$4$		0			0
$5$	0.461663	−	0.266541i	0.206462	−	0.119201i	−0.393204	−	0.919451i	$-0.628633\pi$
$5$	0.461663	−	0.266541i	0.206462	−	0.119201i	0.599666	+	0.800250i	$0.295300\pi$
$6$		0			0
$7$	−0.489180	−	2.60014i	−0.184893	−	0.982759i
$7$	−0.489180	−	2.60014i	−0.184893	−	0.982759i
$8$		0			0
$9$	−2.99339	+	0.198972i	−0.997798	+	0.0663241i
$10$		0			0
$11$	2.28733	−	3.96177i	0.689656	−	1.19452i	−0.282293	−	0.959328i	$-0.591095\pi$
$11$	2.28733	−	3.96177i	0.689656	−	1.19452i	0.971949	−	0.235191i	$-0.0755716\pi$
$12$		0			0
$13$	4.97924			1.38099			0.690496	−	0.723336i	$-0.257392\pi$
$13$	4.97924			1.38099			0.690496	+	0.723336i	$0.257392\pi$
$14$		0			0
$15$	0.487941	+	0.783866i	0.125986	+	0.202393i
$16$		0			0
$17$	2.16139	−	3.74363i	0.524213	−	0.907964i	−0.475389	−	0.879775i	$-0.657693\pi$
$17$	2.16139	−	3.74363i	0.524213	−	0.907964i	0.999603	−	0.0281884i	$-0.00897383\pi$
$18$		0			0
$19$	0.921087	+	1.59537i	0.211312	+	0.366003i	0.952125	−	0.305708i	$-0.0988931\pi$
$19$	0.921087	+	1.59537i	0.211312	+	0.366003i	−0.740814	+	0.671711i	$0.765560\pi$
$20$		0			0
$21$	4.47297	−	0.996248i	0.976083	−	0.217399i
$22$		0			0
$23$	0.103387	−	0.0596907i	0.0215577	−	0.0124464i	−0.489182	−	0.872182i	$-0.662705\pi$
$23$	0.103387	−	0.0596907i	0.0215577	−	0.0124464i	0.510740	+	0.859735i	$0.329371\pi$
$24$		0			0
$25$	−2.35791	+	4.08402i	−0.471582	+	0.816804i
$26$		0			0
$27$	−0.516471	−	5.17042i	−0.0993949	−	0.995048i
$28$		0			0
$29$	7.74542			1.43829			0.719144	−	0.694861i	$-0.244534\pi$
$29$	7.74542			1.43829			0.719144	+	0.694861i	$0.244534\pi$
$30$		0			0
$31$	1.93668	+	1.11814i	0.347838	+	0.200825i	0.663733	−	0.747970i	$-0.268971\pi$
$31$	1.93668	+	1.11814i	0.347838	+	0.200825i	−0.315894	+	0.948794i	$0.602305\pi$
$32$		0			0
$33$	6.98966	+	3.73191i	1.21674	+	0.649642i
$34$		0			0
$35$	−0.918880	−	1.07000i	−0.155319	−	0.180863i
$36$		0			0
$37$	−7.02261	+	4.05451i	−1.15451	+	0.666557i	−0.949982	−	0.312304i	$-0.898899\pi$
$37$	−7.02261	+	4.05451i	−1.15451	+	0.666557i	−0.204528	+	0.978861i	$0.565566\pi$
$38$		0			0
$39$	0.286157	+	8.61955i	0.0458218	+	1.38023i
$40$		0			0
$41$	−2.60914			−0.407479			−0.203740	−	0.979025i	$-0.565310\pi$
$41$	−2.60914			−0.407479			−0.203740	+	0.979025i	$0.565310\pi$
$42$		0			0
$43$			1.87217i			0.285503i	0.989759	+	0.142752i	$0.0455950\pi$
$43$			1.87217i			0.285503i	−0.989759	+	0.142752i	$0.954405\pi$
$44$		0			0
$45$	−1.32891	+	0.889722i	−0.198102	+	0.132632i
$46$		0			0
$47$	−2.91482	−	5.04861i	−0.425170	−	0.736415i	0.571267	−	0.820764i	$-0.306452\pi$
$47$	−2.91482	−	5.04861i	−0.425170	−	0.736415i	−0.996436	+	0.0843492i	$0.973119\pi$
$48$		0			0
$49$	−6.52141	+	2.54387i	−0.931629	+	0.363410i
$50$		0			0
$51$	6.60480	+	3.52642i	0.924857	+	0.493798i
$52$		0			0
$53$	2.29287	−	3.97137i	0.314950	−	0.545510i	−0.664476	−	0.747309i	$-0.731345\pi$
$53$	2.29287	−	3.97137i	0.314950	−	0.545510i	0.979427	+	0.201799i	$0.0646788\pi$
$54$		0			0
$55$		−	2.43867i		−	0.328830i
$56$		0			0
$57$	−2.70880	+	1.68618i	−0.358790	+	0.223339i
$58$		0			0
$59$	5.71492	+	3.29951i	0.744019	+	0.429559i	0.823529	−	0.567275i	$-0.192002\pi$
$59$	5.71492	+	3.29951i	0.744019	+	0.429559i	−0.0795100	+	0.996834i	$0.525336\pi$
$60$		0			0
$61$	−1.07564	−	1.86306i	−0.137722	−	0.238541i	0.788912	−	0.614506i	$-0.210645\pi$
$61$	−1.07564	−	1.86306i	−0.137722	−	0.238541i	−0.926634	+	0.375965i	$0.877311\pi$
$62$		0			0
$63$	1.98166	+	7.68590i	0.249666	+	0.968332i
$64$		0			0
$65$	2.29873	−	1.32717i	0.285123	−	0.164616i
$66$		0			0
$67$	10.4812	+	6.05131i	1.28048	+	0.739285i	0.976936	−	0.213532i	$-0.0684968\pi$
$67$	10.4812	+	6.05131i	1.28048	+	0.739285i	0.303544	+	0.952817i	$0.401830\pi$
$68$		0			0
$69$	0.109272	+	0.175543i	0.0131548	+	0.0211329i
$70$		0			0
$71$		−	6.20627i		−	0.736549i	−0.929717	−	0.368275i	$-0.879949\pi$
$71$		−	6.20627i		−	0.736549i	0.929717	−	0.368275i	$-0.120051\pi$
$72$		0			0
$73$	8.35520	+	4.82388i	0.977902	+	0.564592i	0.901636	−	0.432496i	$-0.142367\pi$
$73$	8.35520	+	4.82388i	0.977902	+	0.564592i	0.0762659	+	0.997088i	$0.475700\pi$
$74$		0			0
$75$	−7.20535	−	3.84706i	−0.832002	−	0.444221i
$76$		0			0
$77$	−11.4201	−	4.00935i	−1.30144	−	0.456908i
$78$		0			0
$79$	0.0228792	+	0.0396280i	0.00257411	+	0.00445849i	0.867310	−	0.497769i	$-0.165847\pi$
$79$	0.0228792	+	0.0396280i	0.00257411	+	0.00445849i	−0.864735	+	0.502228i	$0.832514\pi$
$80$		0			0
$81$	8.92082	−	1.19121i	0.991202	−	0.132356i
$82$		0			0
$83$		−	3.86459i		−	0.424194i	−0.977249	−	0.212097i	$-0.931971\pi$
$83$		−	3.86459i		−	0.424194i	0.977249	−	0.212097i	$-0.0680292\pi$
$84$		0			0
$85$		−	2.30440i		−	0.249947i
$86$		0			0
$87$	0.445129	+	13.4081i	0.0477229	+	1.43750i
$88$		0			0
$89$	−8.23362	−	14.2610i	−0.872762	−	1.51167i	−0.859128	−	0.511761i	$-0.828993\pi$
$89$	−8.23362	−	14.2610i	−0.872762	−	1.51167i	−0.0136336	−	0.999907i	$-0.504340\pi$
$90$		0			0
$91$	−2.43575	−	12.9467i	−0.255335	−	1.35718i
$92$		0			0
$93$	−1.82431	+	3.41684i	−0.189173	+	0.354310i
$94$		0			0
$95$	0.850463	+	0.491015i	0.0872557	+	0.0503771i
$96$		0			0
$97$		−	7.18828i		−	0.729859i	−0.931035	−	0.364930i	$-0.881093\pi$
$97$		−	7.18828i		−	0.729859i	0.931035	−	0.364930i	$-0.118907\pi$
$98$		0			0
$99$	−6.05860	+	12.3143i	−0.608912	+	1.23763i
$100$		0			0
$101$	−3.33419	−	1.92499i	−0.331764	−	0.191544i	0.324860	−	0.945762i	$-0.394683\pi$
$101$	−3.33419	−	1.92499i	−0.331764	−	0.191544i	−0.656624	+	0.754218i	$0.728016\pi$
$102$		0			0
$103$	4.61020	−	2.66170i	0.454256	−	0.262265i	−0.255370	−	0.966843i	$-0.582197\pi$
$103$	4.61020	−	2.66170i	0.454256	−	0.262265i	0.709626	+	0.704578i	$0.248864\pi$
$104$		0			0
$105$	1.79947	−	1.65216i	0.175610	−	0.161235i
$106$		0			0
$107$	4.60634	+	7.97842i	0.445312	+	0.771303i	0.998074	−	0.0620363i	$-0.0197594\pi$
$107$	4.60634	+	7.97842i	0.445312	+	0.771303i	−0.552762	+	0.833339i	$0.686426\pi$
$108$		0			0
$109$	−4.24194	−	2.44909i	−0.406304	−	0.234580i	0.282896	−	0.959151i	$-0.408705\pi$
$109$	−4.24194	−	2.44909i	−0.406304	−	0.234580i	−0.689201	+	0.724571i	$0.742038\pi$
$110$		0			0
$111$	−7.42233	−	11.9238i	−0.704497	−	1.13176i
$112$		0			0
$113$			3.87615i			0.364637i	0.983240	+	0.182319i	$0.0583602\pi$
$113$			3.87615i			0.364637i	−0.983240	+	0.182319i	$0.941640\pi$
$114$		0			0
$115$	0.0318201	−	0.0551140i	0.00296724	−	0.00513941i
$116$		0			0
$117$	−14.9048	+	0.990731i	−1.37795	+	0.0915932i
$118$		0			0
$119$	−10.7913	−	3.78859i	−0.989233	−	0.347299i
$120$		0			0
$121$	−4.96376	−	8.59748i	−0.451251	−	0.781589i
$122$		0			0
$123$	−0.149947	−	4.51667i	−0.0135203	−	0.407255i
$124$		0			0
$125$			5.17934i			0.463254i
$126$		0			0
$127$	−8.19005			−0.726750			−0.363375	−	0.931643i	$-0.618376\pi$
$127$	−8.19005			−0.726750			−0.363375	+	0.931643i	$0.618376\pi$
$128$		0			0
$129$	−3.24091	+	0.107594i	−0.285346	+	0.00947310i
$130$		0			0
$131$	−18.5565	+	10.7136i	−1.62129	+	0.936053i	−0.634715	+	0.772746i	$0.718883\pi$
$131$	−18.5565	+	10.7136i	−1.62129	+	0.936053i	−0.986575	+	0.163306i	$0.947784\pi$
$132$		0			0
$133$	3.69760	−	3.17537i	0.320622	−	0.275340i
$134$		0			0
$135$	−1.61657	−	2.24933i	−0.139132	−	0.193592i
$136$		0			0
$137$	−3.91533	−	2.26052i	−0.334509	−	0.193129i	0.323332	−	0.946286i	$-0.395197\pi$
$137$	−3.91533	−	2.26052i	−0.334509	−	0.193129i	−0.657841	+	0.753157i	$0.728530\pi$
$138$		0			0
$139$	−14.8300			−1.25786			−0.628931	−	0.777461i	$-0.716507\pi$
$139$	−14.8300			−1.25786			−0.628931	+	0.777461i	$0.716507\pi$
$140$		0			0
$141$	8.57212	−	5.33597i	0.721903	−	0.449370i
$142$		0			0
$143$	11.3892	−	19.7266i	0.952410	−	1.64962i
$144$		0			0
$145$	3.57577	−	2.06447i	0.296952	−	0.171445i
$146$		0			0
$147$	−4.77847	−	11.1430i	−0.394121	−	0.919058i
$148$		0			0
$149$	10.7714	+	18.6566i	0.882425	+	1.52841i	0.848636	+	0.528977i	$0.177424\pi$
$149$	10.7714	+	18.6566i	0.882425	+	1.52841i	0.0337890	+	0.999429i	$0.489243\pi$
$150$		0			0
$151$	−1.40767	+	2.43816i	−0.114555	+	0.198415i	−0.917602	−	0.397501i	$-0.869878\pi$
$151$	−1.40767	+	2.43816i	−0.114555	+	0.198415i	0.803047	+	0.595916i	$0.203211\pi$
$152$		0			0
$153$	−5.72500	+	11.6362i	−0.462839	+	0.940733i
$154$		0			0
$155$	1.19213			0.0957539
$156$		0			0
$157$	−3.54427	+	6.13885i	−0.282863	+	0.489933i	−0.972089	−	0.234613i	$-0.924618\pi$
$157$	−3.54427	+	6.13885i	−0.282863	+	0.489933i	0.689226	+	0.724547i	$0.257951\pi$
$158$		0			0
$159$	7.00661	+	3.74095i	0.555660	+	0.296677i
$160$		0			0
$161$	−0.205779	−	0.239622i	−0.0162176	−	0.0188848i
$162$		0			0
$163$	−5.64257	+	3.25774i	−0.441960	+	0.255166i	−0.704429	−	0.709775i	$-0.748797\pi$
$163$	−5.64257	+	3.25774i	−0.441960	+	0.255166i	0.262469	+	0.964941i	$0.415463\pi$
$164$		0			0
$165$	4.22158	−	0.140151i	0.328649	−	0.0109107i
$166$		0			0
$167$	17.2470			1.33462			0.667308	−	0.744782i	$-0.267447\pi$
$167$	17.2470			1.33462			0.667308	+	0.744782i	$0.267447\pi$
$168$		0			0
$169$	11.7928			0.907141
$170$		0			0
$171$	−3.07461	−	4.59230i	−0.235121	−	0.351182i
$172$		0			0
$173$	−14.5387	+	8.39395i	−1.10536	+	0.638180i	−0.937624	−	0.347652i	$-0.886979\pi$
$173$	−14.5387	+	8.39395i	−1.10536	+	0.638180i	−0.167737	+	0.985832i	$0.553646\pi$
$174$		0			0
$175$	11.7725	+	4.13307i	0.889914	+	0.312430i
$176$		0			0
$177$	−5.38333	+	10.0827i	−0.404636	+	0.757862i
$178$		0			0
$179$	−2.00982	+	3.48110i	−0.150221	+	0.260190i	−0.931309	−	0.364231i	$-0.881332\pi$
$179$	−2.00982	+	3.48110i	−0.150221	+	0.260190i	0.781088	+	0.624421i	$0.214665\pi$
$180$		0			0
$181$	14.8596			1.10451			0.552253	−	0.833676i	$-0.313768\pi$
$181$	14.8596			1.10451			0.552253	+	0.833676i	$0.313768\pi$
$182$		0			0
$183$	3.16332	−	1.96911i	0.233840	−	0.145561i
$184$		0			0
$185$	−2.16139	+	3.74363i	−0.158908	+	0.275237i
$186$		0			0
$187$	−9.88761	−	17.1258i	−0.723053	−	1.25237i
$188$		0			0
$189$	−13.1911	+	3.87216i	−0.959515	+	0.281658i
$190$		0			0
$191$	−17.1154	+	9.88159i	−1.23843	+	0.715006i	−0.968773	−	0.247951i	$-0.920243\pi$
$191$	−17.1154	+	9.88159i	−1.23843	+	0.715006i	−0.269655	+	0.962957i	$0.586910\pi$
$192$		0			0
$193$	−6.29229	+	10.8986i	−0.452929	+	0.784496i	−0.998566	−	0.0535255i	$-0.982954\pi$
$193$	−6.29229	+	10.8986i	−0.452929	+	0.784496i	0.545638	+	0.838021i	$0.316287\pi$
$194$		0			0
$195$	2.42957	+	3.90305i	0.173985	+	0.279504i
$196$		0			0
$197$	−8.41804			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$197$	−8.41804			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$198$		0			0
$199$	−12.3980	−	7.15800i	−0.878873	−	0.507417i	−0.00858618	−	0.999963i	$-0.502733\pi$
$199$	−12.3980	−	7.15800i	−0.878873	−	0.507417i	−0.870287	+	0.492546i	$0.836066\pi$
$200$		0			0
$201$	−9.87305	+	18.4917i	−0.696392	+	1.30430i
$202$		0			0
$203$	−3.78890	−	20.1391i	−0.265929	−	1.41349i
$204$		0			0
$205$	−1.20454	+	0.695443i	−0.0841290	+	0.0485719i
$206$		0			0
$207$	−0.297602	+	0.199249i	−0.0206848	+	0.0138488i
$208$		0			0
$209$	8.42732			0.582930
$210$		0			0
$211$			9.62315i			0.662485i	0.943546	+	0.331243i	$0.107468\pi$
$211$			9.62315i			0.662485i	−0.943546	+	0.331243i	$0.892532\pi$
$212$		0			0
$213$	10.7437	−	0.356675i	0.736144	−	0.0244390i
$214$		0			0
$215$	0.499011	+	0.864312i	0.0340323	+	0.0589456i
$216$		0			0
$217$	1.95994	−	5.58261i	0.133049	−	0.378972i
$218$		0			0
$219$	−7.87042	+	14.7409i	−0.531834	+	0.996097i
$220$		0			0
$221$	10.7621	−	18.6404i	0.723935	−	1.25389i
$222$		0			0
$223$			20.1840i			1.35162i	0.737076	+	0.675810i	$0.236206\pi$
$223$			20.1840i			1.35162i	−0.737076	+	0.675810i	$0.763794\pi$
$224$		0			0
$225$	6.24555	−	12.6942i	0.416370	−	0.846283i
$226$		0			0
$227$	1.03403	+	0.597000i	0.0686313	+	0.0396243i	0.533923	−	0.845533i	$-0.320717\pi$
$227$	1.03403	+	0.597000i	0.0686313	+	0.0396243i	−0.465292	+	0.885157i	$0.654051\pi$
$228$		0			0
$229$	−11.4021	−	19.7490i	−0.753472	−	1.30505i	−0.946130	−	0.323786i	$-0.895044\pi$
$229$	−11.4021	−	19.7490i	−0.753472	−	1.30505i	0.192658	−	0.981266i	$-0.438289\pi$
$230$		0			0
$231$	6.28426	−	19.9996i	0.413474	−	1.31588i
$232$		0			0
$233$	14.1080	−	8.14528i	0.924249	−	0.533615i	0.0392607	−	0.999229i	$-0.487500\pi$
$233$	14.1080	−	8.14528i	0.924249	−	0.533615i	0.884988	+	0.465614i	$0.154166\pi$
$234$		0			0
$235$	−2.69133	−	1.55384i	−0.175563	−	0.101361i
$236$		0			0
$237$	−0.0672850	+	0.0418836i	−0.00437063	+	0.00272063i
$238$		0			0
$239$			20.2417i			1.30933i	0.755920	+	0.654664i	$0.227190\pi$
$239$			20.2417i			1.30933i	−0.755920	+	0.654664i	$0.772810\pi$
$240$		0			0
$241$	−7.99312	−	4.61483i	−0.514882	−	0.297267i	0.219956	−	0.975510i	$-0.429409\pi$
$241$	−7.99312	−	4.61483i	−0.514882	−	0.297267i	−0.734838	+	0.678242i	$0.762742\pi$
$242$		0			0
$243$	2.57477	+	15.3743i	0.165172	+	0.986265i
$244$		0			0
$245$	−2.33265	+	2.91263i	−0.149027	+	0.186081i
$246$		0			0
$247$	4.58631	+	7.94372i	0.291820	+	0.505447i
$248$		0			0
$249$	6.68998	−	0.222098i	0.423960	−	0.0140749i
$250$		0			0
$251$		−	8.22152i		−	0.518938i	−0.965751	−	0.259469i	$-0.916452\pi$
$251$		−	8.22152i		−	0.518938i	0.965751	−	0.259469i	$-0.0835475\pi$
$252$		0			0
$253$		−	0.546129i		−	0.0343349i
$254$		0			0
$255$	3.98913	−	0.132434i	0.249809	−	0.00829332i
$256$		0			0
$257$	−6.71468	−	11.6302i	−0.418850	−	0.725470i	0.576974	−	0.816763i	$-0.304233\pi$
$257$	−6.71468	−	11.6302i	−0.418850	−	0.725470i	−0.995824	+	0.0912928i	$0.970900\pi$
$258$		0			0
$259$	13.9776	+	16.2763i	0.868525	+	1.01136i
$260$		0			0
$261$	−23.1851	+	1.54112i	−1.43512	+	0.0953932i
$262$		0			0
$263$	−13.0415	−	7.52949i	−0.804170	−	0.464288i	0.0407569	−	0.999169i	$-0.487023\pi$
$263$	−13.0415	−	7.52949i	−0.804170	−	0.464288i	−0.844927	+	0.534881i	$0.820356\pi$
$264$		0			0
$265$		−	2.44458i		−	0.150170i
$266$		0			0
$267$	24.2141	−	15.0728i	1.48188	−	0.922439i
$268$		0			0
$269$	11.5014	+	6.64035i	0.701254	+	0.404869i	0.807814	−	0.589437i	$-0.200650\pi$
$269$	11.5014	+	6.64035i	0.701254	+	0.404869i	−0.106560	+	0.994306i	$0.533984\pi$
$270$		0			0
$271$	−16.2954	+	9.40818i	−0.989878	+	0.571506i	−0.905238	−	0.424905i	$-0.860307\pi$
$271$	−16.2954	+	9.40818i	−0.989878	+	0.571506i	−0.0846401	+	0.996412i	$0.526974\pi$
$272$		0			0
$273$	22.2720	−	4.96056i	1.34796	−	0.300227i
$274$		0			0
$275$	10.7866	+	18.6830i	0.650459	+	1.12663i
$276$		0			0
$277$	20.1344	+	11.6246i	1.20976	+	0.698454i	0.962706	−	0.270548i	$-0.0872049\pi$
$277$	20.1344	+	11.6246i	1.20976	+	0.698454i	0.247052	+	0.969002i	$0.420538\pi$
$278$		0			0
$279$	−6.01973	−	2.96170i	−0.360392	−	0.177312i
$280$		0			0
$281$			21.2736i			1.26908i	0.772892	+	0.634538i	$0.218810\pi$
$281$			21.2736i			1.26908i	−0.772892	+	0.634538i	$0.781190\pi$
$282$		0			0
$283$	4.31186	−	7.46836i	0.256314	−	0.443948i	−0.708938	−	0.705271i	$-0.750825\pi$
$283$	4.31186	−	7.46836i	0.256314	−	0.443948i	0.965251	+	0.261323i	$0.0841587\pi$
$284$		0			0
$285$	−0.801119	+	1.50045i	−0.0474542	+	0.0888792i
$286$		0			0
$287$	1.27634	+	6.78411i	0.0753399	+	0.400454i
$288$		0			0
$289$	−0.843181	−	1.46043i	−0.0495989	−	0.0859078i
$290$		0			0
$291$	12.4436	−	0.413111i	0.729457	−	0.0242170i
$292$		0			0
$293$		−	22.7441i		−	1.32872i	−0.747411	−	0.664362i	$-0.768703\pi$
$293$		−	22.7441i		−	1.32872i	0.747411	−	0.664362i	$-0.231297\pi$
$294$		0			0
$295$	3.51782			0.204815
$296$		0			0
$297$	−21.6654	−	9.78032i	−1.25715	−	0.567512i
$298$		0			0
$299$	0.514790	−	0.297214i	0.0297711	−	0.0171883i
$300$		0			0
$301$	4.86790	−	0.915828i	0.280581	−	0.0527875i
$302$		0			0
$303$	3.14074	−	5.88243i	0.180431	−	0.337937i
$304$		0			0
$305$	−0.993166	−	0.573405i	−0.0568685	−	0.0328331i
$306$		0			0
$307$	22.8169			1.30223			0.651114	−	0.758980i	$-0.274302\pi$
$307$	22.8169			1.30223			0.651114	+	0.758980i	$0.274302\pi$
$308$		0			0
$309$	4.87261	+	7.82773i	0.277193	+	0.445304i
$310$		0			0
$311$	−11.9871	+	20.7622i	−0.679725	+	1.17732i	0.295339	+	0.955393i	$0.404567\pi$
$311$	−11.9871	+	20.7622i	−0.679725	+	1.17732i	−0.975064	+	0.221925i	$0.928766\pi$
$312$		0			0
$313$	19.4419	−	11.2248i	1.09892	−	0.634463i	0.162984	−	0.986629i	$-0.447888\pi$
$313$	19.4419	−	11.2248i	1.09892	−	0.634463i	0.935938	+	0.352166i	$0.114555\pi$
$314$		0			0
$315$	2.96347	+	3.02010i	0.166973	+	0.170163i
$316$		0			0
$317$	1.06072	+	1.83723i	0.0595762	+	0.103189i	0.894275	−	0.447517i	$-0.147692\pi$
$317$	1.06072	+	1.83723i	0.0595762	+	0.103189i	−0.834699	+	0.550706i	$0.814358\pi$
$318$		0			0
$319$	17.7163	−	30.6856i	0.991924	−	1.71806i
$320$		0			0
$321$	−13.5467	+	8.43255i	−0.756103	+	0.470659i
$322$		0			0
$323$	7.96330			0.443090
$324$		0			0
$325$	−11.7406	+	20.3353i	−0.651252	+	1.12800i
$326$		0			0
$327$	3.99582	−	7.48396i	0.220969	−	0.413864i
$328$		0			0
$329$	−11.7012	+	10.0486i	−0.645108	+	0.553997i
$330$		0			0
$331$	−1.25478	+	0.724448i	−0.0689689	+	0.0398192i	−0.534088	−	0.845429i	$-0.679345\pi$
$331$	−1.25478	+	0.724448i	−0.0689689	+	0.0398192i	0.465119	+	0.885248i	$0.346012\pi$
$332$		0			0
$333$	20.2147	−	13.5340i	1.10776	−	0.741661i
$334$		0			0
$335$	6.45170			0.352494
$336$		0			0
$337$	−21.6680			−1.18033			−0.590165	−	0.807282i	$-0.700937\pi$
$337$	−21.6680			−1.18033			−0.590165	+	0.807282i	$0.700937\pi$
$338$		0			0
$339$	−6.70999	+	0.222762i	−0.364436	+	0.0120988i
$340$		0			0
$341$	8.85966	−	5.11513i	0.479778	−	0.277000i
$342$		0			0
$343$	9.80454	+	15.7121i	0.529396	+	0.848375i
$344$		0			0
$345$	0.0972364	+	0.0519162i	0.00523503	+	0.00279508i
$346$		0			0
$347$	13.7374	−	23.7939i	0.737463	−	1.27732i	−0.216171	−	0.976356i	$-0.569357\pi$
$347$	13.7374	−	23.7939i	0.737463	−	1.27732i	0.953634	−	0.300969i	$-0.0973099\pi$
$348$		0			0
$349$	−15.6203			−0.836134			−0.418067	−	0.908416i	$-0.637292\pi$
$349$	−15.6203			−0.836134			−0.418067	+	0.908416i	$0.637292\pi$
$350$		0			0
$351$	−2.57163	−	25.7448i	−0.137264	−	1.37415i
$352$		0			0
$353$	−6.72613	+	11.6500i	−0.357996	+	0.620067i	−0.987626	−	0.156828i	$-0.949873\pi$
$353$	−6.72613	+	11.6500i	−0.357996	+	0.620067i	0.629630	+	0.776895i	$0.283207\pi$
$354$		0			0
$355$	−1.65423	−	2.86521i	−0.0877973	−	0.152069i
$356$		0			0
$357$	5.93824	−	18.8984i	0.314285	−	1.00021i
$358$		0			0
$359$	19.9816	−	11.5364i	1.05459	−	0.608867i	0.130658	−	0.991428i	$-0.458291\pi$
$359$	19.9816	−	11.5364i	1.05459	−	0.608867i	0.923930	+	0.382561i	$0.124958\pi$
$360$		0			0
$361$	7.80320	−	13.5155i	0.410695	−	0.711344i
$362$		0			0
$363$	14.5978	−	9.08684i	0.766186	−	0.476936i
$364$		0			0
$365$	5.14305			0.269200
$366$		0			0
$367$	−18.6893	−	10.7903i	−0.975574	−	0.563248i	−0.0746427	−	0.997210i	$-0.523782\pi$
$367$	−18.6893	−	10.7903i	−0.975574	−	0.563248i	−0.900931	+	0.433963i	$0.857115\pi$
$368$		0			0
$369$	7.81018	−	0.519147i	0.406582	−	0.0270257i
$370$		0			0
$371$	−11.4477	−	4.01907i	−0.594337	−	0.208659i
$372$		0			0
$373$	−0.158888	+	0.0917338i	−0.00822689	+	0.00474980i	−0.504108	−	0.863641i	$-0.668179\pi$
$373$	−0.158888	+	0.0917338i	−0.00822689	+	0.00474980i	0.495881	+	0.868391i	$0.334845\pi$
$374$		0			0
$375$	−8.96593	+	0.297657i	−0.462999	+	0.0153709i
$376$		0			0
$377$	38.5663			1.98627
$378$		0			0
$379$			2.93359i			0.150688i	0.997158	+	0.0753441i	$0.0240055\pi$
$379$			2.93359i			0.150688i	−0.997158	+	0.0753441i	$0.975994\pi$
$380$		0			0
$381$	−0.470683	−	14.1778i	−0.0241138	−	0.726349i
$382$		0			0
$383$	−7.67488	−	13.2933i	−0.392168	−	0.679255i	0.600567	−	0.799574i	$-0.294942\pi$
$383$	−7.67488	−	13.2933i	−0.392168	−	0.679255i	−0.992735	+	0.120319i	$0.961608\pi$
$384$		0			0
$385$	−6.34088	+	1.19295i	−0.323161	+	0.0607983i
$386$		0			0
$387$	−0.372510	−	5.60414i	−0.0189358	−	0.284875i
$388$		0			0
$389$	−2.00060	+	3.46513i	−0.101434	+	0.175689i	−0.912276	−	0.409577i	$-0.865676\pi$
$389$	−2.00060	+	3.46513i	−0.101434	+	0.175689i	0.810842	+	0.585266i	$0.199010\pi$
$390$		0			0
$391$		−	0.516059i		−	0.0260982i
$392$		0			0
$393$	−19.6127	−	31.5074i	−0.989332	−	1.58934i
$394$		0			0
$395$	0.0211250	+	0.0121965i	0.00106291	+	0.000613673i
$396$		0			0
$397$	11.7195	+	20.2987i	0.588183	+	1.01876i	0.994470	+	0.105017i	$0.0334897\pi$
$397$	11.7195	+	20.2987i	0.588183	+	1.01876i	−0.406288	+	0.913745i	$0.633177\pi$
$398$		0			0
$399$	5.70938	+	6.21841i	0.285826	+	0.311310i
$400$		0			0
$401$	−14.5441	+	8.39703i	−0.726297	+	0.419328i	−0.817066	−	0.576544i	$-0.804401\pi$
$401$	−14.5441	+	8.39703i	−0.726297	+	0.419328i	0.0907689	+	0.995872i	$0.471068\pi$
$402$		0			0
$403$	9.64320	+	5.56751i	0.480362	+	0.277337i
$404$		0			0
$405$	3.80091	−	2.92770i	0.188869	−	0.145479i
$406$		0			0
$407$			37.0960i			1.83878i
$408$		0			0
$409$	11.9749	+	6.91372i	0.592121	+	0.341861i	0.765936	−	0.642917i	$-0.222276\pi$
$409$	11.9749	+	6.91372i	0.592121	+	0.341861i	−0.173815	+	0.984778i	$0.555609\pi$
$410$		0			0
$411$	3.68816	−	6.90773i	0.181924	−	0.340733i
$412$		0			0
$413$	5.78354	−	16.4736i	0.284590	−	0.810613i
$414$		0			0
$415$	−1.03007	−	1.78414i	−0.0505643	−	0.0875799i
$416$		0			0
$417$	−0.852279	−	25.6721i	−0.0417363	−	1.25717i
$418$		0			0
$419$			17.5573i			0.857728i	0.903369	+	0.428864i	$0.141086\pi$
$419$			17.5573i			0.857728i	−0.903369	+	0.428864i	$0.858914\pi$
$420$		0			0
$421$			19.8896i			0.969362i	0.874691	+	0.484681i	$0.161064\pi$
$421$			19.8896i			0.969362i	−0.874691	+	0.484681i	$0.838936\pi$
$422$		0			0
$423$	9.72973	+	14.5325i	0.473075	+	0.706595i
$424$		0			0
$425$	10.1927	+	17.6543i	0.494419	+	0.856359i
$426$		0			0
$427$	−4.31803	+	3.70818i	−0.208964	+	0.179451i
$428$		0			0
$429$	34.8032	+	18.5821i	1.68032	+	0.897150i
$430$		0			0
$431$	25.3821	+	14.6544i	1.22261	+	0.705876i	0.965474	−	0.260498i	$-0.0838868\pi$
$431$	25.3821	+	14.6544i	1.22261	+	0.705876i	0.257139	+	0.966374i	$0.417220\pi$
$432$		0			0
$433$			12.5427i			0.602763i	0.953504	+	0.301381i	$0.0974477\pi$
$433$			12.5427i			0.602763i	−0.953504	+	0.301381i	$0.902552\pi$
$434$		0			0
$435$	3.77930	+	6.07137i	0.181204	+	0.291100i
$436$		0			0
$437$	0.190457	+	0.109961i	0.00911081	+	0.00526013i
$438$		0			0
$439$	−11.7921	+	6.80818i	−0.562807	+	0.324937i	−0.754271	−	0.656563i	$-0.772010\pi$
$439$	−11.7921	+	6.80818i	−0.562807	+	0.324937i	0.191464	+	0.981500i	$0.438676\pi$
$440$		0			0
$441$	19.0150	−	8.91238i	0.905475	−	0.424399i
$442$		0			0
$443$	−6.72205	−	11.6429i	−0.319374	−	0.553172i	0.660984	−	0.750400i	$-0.270139\pi$
$443$	−6.72205	−	11.6429i	−0.319374	−	0.553172i	−0.980358	+	0.197228i	$0.936806\pi$
$444$		0			0
$445$	−7.60232	−	4.38920i	−0.360384	−	0.208068i
$446$		0			0
$447$	−31.6773	+	19.7185i	−1.49828	+	0.932653i
$448$		0			0
$449$			16.3428i			0.771266i	0.922652	+	0.385633i	$0.126017\pi$
$449$			16.3428i			0.771266i	−0.922652	+	0.385633i	$0.873983\pi$
$450$		0			0
$451$	−5.96796	+	10.3368i	−0.281020	+	0.486742i
$452$		0			0
$453$	−4.30160	−	2.29670i	−0.202107	−	0.107908i
$454$		0			0
$455$	−4.57532	−	5.32779i	−0.214494	−	0.249770i
$456$		0			0
$457$	14.6395	+	25.3564i	0.684808	+	1.18612i	0.973497	+	0.228699i	$0.0734472\pi$
$457$	14.6395	+	25.3564i	0.684808	+	1.18612i	−0.288689	+	0.957423i	$0.593219\pi$
$458$		0			0
$459$	−20.4724	−	9.24180i	−0.955572	−	0.431370i
$460$		0			0
$461$			6.06975i			0.282696i	0.989960	+	0.141348i	$0.0451437\pi$
$461$			6.06975i			0.282696i	−0.989960	+	0.141348i	$0.954856\pi$
$462$		0			0
$463$	3.30400			0.153550			0.0767750	−	0.997048i	$-0.475538\pi$
$463$	3.30400			0.153550			0.0767750	+	0.997048i	$0.475538\pi$
$464$		0			0
$465$	0.0685115	+	2.06369i	0.00317715	+	0.0957011i
$466$		0			0
$467$	7.03895	−	4.06394i	0.325724	−	0.188057i	−0.328217	−	0.944602i	$-0.606448\pi$
$467$	7.03895	−	4.06394i	0.325724	−	0.188057i	0.653941	+	0.756546i	$0.273114\pi$
$468$		0			0
$469$	10.6070	−	30.2127i	0.489788	−	1.39509i
$470$		0			0
$471$	−10.8306	−	5.78267i	−0.499049	−	0.266451i
$472$		0			0
$473$	7.41711	+	4.28227i	0.341039	+	0.196899i
$474$		0			0
$475$	−8.68736			−0.398604
$476$		0			0
$477$	−6.07328	+	12.3441i	−0.278076	+	0.565198i
$478$		0			0
$479$	−0.425876	+	0.737638i	−0.0194588	+	0.0337035i	−0.875591	−	0.483054i	$-0.839528\pi$
$479$	−0.425876	+	0.737638i	−0.0194588	+	0.0337035i	0.856132	+	0.516757i	$0.172861\pi$
$480$		0			0
$481$	−34.9673	+	20.1884i	−1.59437	+	0.920510i
$482$		0			0
$483$	0.402982	−	0.369994i	0.0183363	−	0.0168353i
$484$		0			0
$485$	−1.91597	−	3.31856i	−0.0869999	−	0.150688i
$486$		0			0
$487$	2.45804	−	4.25745i	0.111384	−	0.192923i	−0.804944	−	0.593350i	$-0.797805\pi$
$487$	2.45804	−	4.25745i	0.111384	−	0.192923i	0.916329	+	0.400427i	$0.131138\pi$
$488$		0			0
$489$	−5.96374	−	9.58062i	−0.269690	−	0.433250i
$490$		0			0
$491$	5.07434			0.229002			0.114501	−	0.993423i	$-0.463473\pi$
$491$	5.07434			0.229002			0.114501	+	0.993423i	$0.463473\pi$
$492$		0			0
$493$	16.7408	−	28.9960i	0.753970	−	1.30591i
$494$		0			0
$495$	0.485228	+	7.29991i	0.0218094	+	0.328106i
$496$		0			0
$497$	−16.1372	+	3.03599i	−0.723850	+	0.136183i
$498$		0			0
$499$	−17.6743	+	10.2042i	−0.791209	+	0.456805i	−0.840388	−	0.541985i	$-0.817673\pi$
$499$	−17.6743	+	10.2042i	−0.791209	+	0.456805i	0.0491790	+	0.998790i	$0.484340\pi$
$500$		0			0
$501$	0.991187	+	29.8563i	0.0442830	+	1.33388i
$502$		0			0
$503$	26.6102			1.18649			0.593245	−	0.805022i	$-0.297847\pi$
$503$	26.6102			1.18649			0.593245	+	0.805022i	$0.297847\pi$
$504$		0			0
$505$	−2.05236			−0.0913289
$506$		0			0
$507$	0.677734	+	20.4145i	0.0300992	+	0.906641i
$508$		0			0
$509$	−24.9978	+	14.4325i	−1.10801	+	0.639710i	−0.938313	−	0.345787i	$-0.887612\pi$
$509$	−24.9978	+	14.4325i	−1.10801	+	0.639710i	−0.169697	+	0.985496i	$0.554279\pi$
$510$		0			0
$511$	8.45553	−	24.0844i	0.374051	−	1.06543i
$512$		0			0
$513$	7.77301	−	5.58637i	0.343187	−	0.246644i
$514$		0			0
$515$	1.41891	−	2.45762i	0.0625245	−	0.108296i
$516$		0			0
$517$	−26.6686			−1.17288
$518$		0			0
$519$	−15.3663	−	24.6856i	−0.674505	−	1.08358i
$520$		0			0
$521$	12.5564	−	21.7483i	0.550105	−	0.952811i	−0.448161	−	0.893953i	$-0.647921\pi$
$521$	12.5564	−	21.7483i	0.550105	−	0.952811i	0.998266	−	0.0588577i	$-0.0187458\pi$
$522$		0			0
$523$	−1.54754	−	2.68042i	−0.0676692	−	0.117206i	0.830206	−	0.557457i	$-0.188223\pi$
$523$	−1.54754	−	2.68042i	−0.0676692	−	0.117206i	−0.897875	+	0.440251i	$0.854890\pi$
$524$		0			0
$525$	−6.47818	+	20.6168i	−0.282731	+	0.899790i
$526$		0			0
$527$	8.37183	−	4.83348i	0.364683	−	0.210550i
$528$		0			0
$529$	−11.4929	+	19.9062i	−0.499690	+	0.865489i
$530$		0			0
$531$	−17.7635	−	8.73962i	−0.770871	−	0.379267i
$532$		0			0
$533$	−12.9915			−0.562726
$534$		0			0
$535$	4.25316	+	2.45556i	0.183880	+	0.106163i
$536$		0			0
$537$	−6.14163	−	3.27913i	−0.265031	−	0.141505i
$538$		0			0
$539$	−4.83838	+	31.6550i	−0.208404	+	1.36348i
$540$		0			0
$541$	23.8925	−	13.7944i	1.02722	−	0.593066i	0.111033	−	0.993817i	$-0.464584\pi$
$541$	23.8925	−	13.7944i	1.02722	−	0.593066i	0.916187	+	0.400751i	$0.131251\pi$
$542$		0			0
$543$	0.853983	+	25.7234i	0.0366479	+	1.10390i
$544$		0			0
$545$	−2.61113			−0.111849
$546$		0			0
$547$		−	32.0757i		−	1.37146i	−0.727856	−	0.685730i	$-0.759483\pi$
$547$		−	32.0757i		−	1.37146i	0.727856	−	0.685730i	$-0.240517\pi$
$548$		0			0
$549$	3.59051	+	5.36286i	0.153239	+	0.228881i
$550$		0			0
$551$	7.13420	+	12.3568i	0.303927	+	0.526417i
$552$		0			0
$553$	0.0918460	−	0.0788743i	0.00390569	−	0.00335407i
$554$		0			0
$555$	−6.60480	−	3.52642i	−0.280358	−	0.149688i
$556$		0			0
$557$	−8.23577	+	14.2648i	−0.348961	+	0.604417i	−0.986065	−	0.166360i	$-0.946799\pi$
$557$	−8.23577	+	14.2648i	−0.348961	+	0.604417i	0.637104	+	0.770777i	$0.280132\pi$
$558$		0			0
$559$			9.32199i			0.394278i
$560$		0			0
$561$	29.0782	−	18.1006i	1.22768	−	0.764209i
$562$		0			0
$563$	−14.5542	−	8.40290i	−0.613388	−	0.354140i	0.160902	−	0.986970i	$-0.448560\pi$
$563$	−14.5542	−	8.40290i	−0.613388	−	0.354140i	−0.774290	+	0.632830i	$0.781893\pi$
$564$		0			0
$565$	1.03315	+	1.78947i	0.0434651	+	0.0752837i
$566$		0			0
$567$	−7.46118	−	22.6126i	−0.313340	−	0.949641i
$568$		0			0
$569$	−32.1947	+	18.5876i	−1.34967	+	0.779235i	−0.988203	−	0.153149i	$-0.951059\pi$
$569$	−32.1947	+	18.5876i	−1.34967	+	0.779235i	−0.361471	+	0.932383i	$0.617725\pi$
$570$		0			0
$571$	6.80801	+	3.93061i	0.284906	+	0.164491i	0.635642	−	0.771984i	$-0.280735\pi$
$571$	6.80801	+	3.93061i	0.284906	+	0.164491i	−0.350736	+	0.936474i	$0.614069\pi$
$572$		0			0
$573$	−18.0896	−	29.0605i	−0.755704	−	1.21402i
$574$		0			0
$575$			0.562982i			0.0234780i
$576$		0			0
$577$	14.7236	+	8.50067i	0.612951	+	0.353888i	0.774120	−	0.633039i	$-0.218193\pi$
$577$	14.7236	+	8.50067i	0.612951	+	0.353888i	−0.161168	+	0.986927i	$0.551526\pi$
$578$		0			0
$579$	−19.2281	−	10.2662i	−0.799092	−	0.426650i
$580$		0			0
$581$	−10.0484	+	1.89048i	−0.416880	+	0.0784303i
$582$		0			0
$583$	−10.4891	−	18.1677i	−0.434415	−	0.752429i
$584$		0			0
$585$	−6.61694	+	4.43014i	−0.273577	+	0.183164i
$586$		0			0
$587$			24.3750i			1.00606i	0.864268	+	0.503032i	$0.167782\pi$
$587$			24.3750i			1.00606i	−0.864268	+	0.503032i	$0.832218\pi$
$588$		0			0
$589$			4.11963i			0.169746i
$590$		0			0
$591$	−0.483785	−	14.5724i	−0.0199003	−	0.599430i
$592$		0			0
$593$	0.0286004	+	0.0495374i	0.00117448	+	0.00203426i	0.866612	−	0.498983i	$-0.166293\pi$
$593$	0.0286004	+	0.0495374i	0.00117448	+	0.00203426i	−0.865438	+	0.501017i	$0.832959\pi$
$594$		0			0
$595$	−5.99174	+	1.12726i	−0.245637	+	0.0462133i
$596$		0			0
$597$	11.6787	−	21.8736i	0.477977	−	0.895225i
$598$		0			0
$599$	−35.8620	−	20.7049i	−1.46528	−	0.845980i	−0.466033	−	0.884768i	$-0.654317\pi$
$599$	−35.8620	−	20.7049i	−1.46528	−	0.845980i	−0.999247	+	0.0387877i	$0.987650\pi$
$600$		0			0
$601$		−	23.8559i		−	0.973104i	−0.873652	−	0.486552i	$-0.838254\pi$
$601$		−	23.8559i		−	0.973104i	0.873652	−	0.486552i	$-0.161746\pi$
$602$		0			0
$603$	−32.5783	−	16.0285i	−1.32669	−	0.652731i
$604$		0			0
$605$	−4.58317	−	2.64609i	−0.186332	−	0.107579i
$606$		0			0
$607$	33.6542	−	19.4303i	1.36598	−	0.788650i	0.375570	−	0.926794i	$-0.377447\pi$
$607$	33.6542	−	19.4303i	1.36598	−	0.788650i	0.990412	+	0.138144i	$0.0441136\pi$
$608$		0			0
$609$	34.6450	−	7.71636i	1.40389	−	0.312683i
$610$		0			0
$611$	−14.5136	−	25.1382i	−0.587156	−	1.01698i
$612$		0			0
$613$	−16.8751	−	9.74286i	−0.681580	−	0.393510i	0.118870	−	0.992910i	$-0.462073\pi$
$613$	−16.8751	−	9.74286i	−0.681580	−	0.393510i	−0.800450	+	0.599400i	$0.795406\pi$
$614$		0			0
$615$	−1.27311	−	2.04521i	−0.0513366	−	0.0824710i
$616$		0			0
$617$			21.5819i			0.868854i	0.900707	+	0.434427i	$0.143049\pi$
$617$			21.5819i			0.868854i	−0.900707	+	0.434427i	$0.856951\pi$
$618$		0			0
$619$	5.60757	−	9.71259i	0.225387	−	0.390382i	−0.731048	−	0.682326i	$-0.760969\pi$
$619$	5.60757	−	9.71259i	0.225387	−	0.390382i	0.956436	+	0.291944i	$0.0943020\pi$
$620$		0			0
$621$	−0.362023	−	0.503728i	−0.0145275	−	0.0202139i
$622$		0			0
$623$	−33.0529	+	28.3847i	−1.32424	+	1.13721i
$624$		0			0
$625$	−10.4090	−	18.0290i	−0.416362	−	0.721160i
$626$		0			0
$627$	0.484318	+	14.5885i	0.0193418	+	0.582609i
$628$		0			0
$629$			35.0534i			1.39767i
$630$		0			0
$631$	22.3220			0.888626			0.444313	−	0.895872i	$-0.353448\pi$
$631$	22.3220			0.888626			0.444313	+	0.895872i	$0.353448\pi$
$632$		0			0
$633$	−16.6586	+	0.553043i	−0.662121	+	0.0219815i
$634$		0			0
$635$	−3.78105	+	2.18299i	−0.150046	+	0.0866292i
$636$		0			0
$637$	−32.4716	+	12.6665i	−1.28657	+	0.501866i
$638$		0			0
$639$	1.23488	+	18.5778i	0.0488510	+	0.734927i
$640$		0			0
$641$	−10.9414	−	6.31703i	−0.432160	−	0.249508i	0.268107	−	0.963389i	$-0.413602\pi$
$641$	−10.9414	−	6.31703i	−0.432160	−	0.249508i	−0.700266	+	0.713882i	$0.746935\pi$
$642$		0			0
$643$	25.9092			1.02176			0.510879	−	0.859652i	$-0.329320\pi$
$643$	25.9092			1.02176			0.510879	+	0.859652i	$0.329320\pi$
$644$		0			0
$645$	−1.46753	+	0.913508i	−0.0577839	+	0.0359693i
$646$		0			0
$647$	8.29783	−	14.3723i	0.326221	−	0.565032i	−0.655538	−	0.755163i	$-0.727558\pi$
$647$	8.29783	−	14.3723i	0.326221	−	0.565032i	0.981759	+	0.190131i	$0.0608912\pi$
$648$		0			0
$649$	26.1438	−	15.0941i	1.02623	−	0.592496i
$650$		0			0
$651$	9.77667	+	3.07201i	0.383178	+	0.120402i
$652$		0			0
$653$	2.57443	+	4.45904i	0.100745	+	0.174496i	0.911992	−	0.410208i	$-0.134544\pi$
$653$	2.57443	+	4.45904i	0.100745	+	0.174496i	−0.811247	+	0.584704i	$0.801211\pi$
$654$		0			0
$655$	−5.71124	+	9.89216i	−0.223157	+	0.386519i
$656$		0			0
$657$	−25.9702	−	12.7773i	−1.01319	−	0.498490i
$658$		0			0
$659$	−20.6891			−0.805934			−0.402967	−	0.915214i	$-0.632021\pi$
$659$	−20.6891			−0.805934			−0.402967	+	0.915214i	$0.632021\pi$
$660$		0			0
$661$	12.3911	−	21.4621i	0.481960	−	0.834779i	−0.517826	−	0.855486i	$-0.673258\pi$
$661$	12.3911	−	21.4621i	0.481960	−	0.834779i	0.999786	+	0.0207072i	$0.00659177\pi$
$662$		0			0
$663$	32.8869	+	17.5589i	1.27722	+	0.681931i
$664$		0			0
$665$	0.860676	−	2.45151i	0.0333756	−	0.0950657i
$666$		0			0
$667$	0.800778	−	0.462329i	0.0310063	−	0.0179015i
$668$		0			0
$669$	−34.9404	+	1.15997i	−1.35088	+	0.0448472i
$670$		0			0
$671$	−9.84137			−0.379922
$672$		0			0
$673$	0.492833			0.0189973			0.00949866	−	0.999955i	$-0.496976\pi$
$673$	0.492833			0.0189973			0.00949866	+	0.999955i	$0.496976\pi$
$674$		0			0
$675$	22.3339	+	10.0821i	0.859633	+	0.388061i
$676$		0			0
$677$	35.2987	−	20.3797i	1.35664	−	0.783256i	0.367471	−	0.930035i	$-0.380224\pi$
$677$	35.2987	−	20.3797i	1.35664	−	0.783256i	0.989169	+	0.146779i	$0.0468905\pi$
$678$		0			0
$679$	−18.6905	+	3.51636i	−0.717276	+	0.134946i
$680$		0			0
$681$	−0.974039	+	1.82432i	−0.0373253	+	0.0699082i
$682$		0			0
$683$	−14.8402	+	25.7039i	−0.567843	+	0.983532i	0.428936	+	0.903335i	$0.358888\pi$
$683$	−14.8402	+	25.7039i	−0.567843	+	0.983532i	−0.996779	+	0.0801976i	$0.974445\pi$
$684$		0			0
$685$	−2.41009			−0.0920846
$686$		0			0
$687$	33.5322	−	20.8731i	1.27933	−	0.796360i
$688$		0			0
$689$	11.4168	−	19.7744i	0.434944	−	0.753346i
$690$		0			0
$691$	3.83116	+	6.63576i	0.145744	+	0.252436i	0.929650	−	0.368443i	$-0.120109\pi$
$691$	3.83116	+	6.63576i	0.145744	+	0.252436i	−0.783906	+	0.620879i	$0.786776\pi$
$692$		0			0
$693$	34.9825	+	9.72928i	1.32887	+	0.369585i
$694$		0			0
$695$	−6.84645	+	3.95280i	−0.259701	+	0.149938i
$696$		0			0
$697$	−5.63936	+	9.76765i	−0.213606	+	0.369976i
$698$		0			0
$699$	14.9111	+	23.9543i	0.563988	+	0.906034i
$700$		0			0
$701$	−6.75507			−0.255136			−0.127568	−	0.991830i	$-0.540717\pi$
$701$	−6.75507			−0.255136			−0.127568	+	0.991830i	$0.540717\pi$
$702$		0			0
$703$	−12.9369	−	7.46910i	−0.487923	−	0.281702i
$704$		0			0
$705$	2.53517	−	4.74825i	0.0954801	−	0.178829i
$706$		0			0
$707$	−3.37423	+	9.61100i	−0.126901	+	0.361459i
$708$		0			0
$709$	−36.0884	+	20.8357i	−1.35533	+	0.782499i	−0.988990	−	0.147982i	$-0.952722\pi$
$709$	−36.0884	+	20.8357i	−1.35533	+	0.782499i	−0.366339	+	0.930482i	$0.619389\pi$
$710$		0			0
$711$	−0.0763714	−	0.114070i	−0.00286415	−	0.00427795i
$712$		0			0
$713$	0.266971			0.00999815
$714$		0			0
$715$		−	12.1427i		−	0.454112i
$716$		0			0
$717$	−35.0404	+	1.16329i	−1.30861	+	0.0434439i
$718$		0			0
$719$	−23.2782	−	40.3190i	−0.868131	−	1.50365i	−0.863904	−	0.503656i	$-0.831988\pi$
$719$	−23.2782	−	40.3190i	−0.868131	−	1.50365i	−0.00422645	−	0.999991i	$-0.501345\pi$
$720$		0			0
$721$	−9.17600	−	10.6851i	−0.341732	−	0.397934i
$722$		0			0
$723$	7.52936	−	14.1021i	0.280020	−	0.524462i
$724$		0			0
$725$	−18.2630	+	31.6325i	−0.678271	+	1.17480i
$726$		0			0
$727$		−	10.7218i		−	0.397651i	−0.980035	−	0.198825i	$-0.936287\pi$
$727$		−	10.7218i		−	0.397651i	0.980035	−	0.198825i	$-0.0637127\pi$
$728$		0			0
$729$	−26.4665	+	5.34075i	−0.980241	+	0.197805i
$730$		0			0
$731$	7.00871	+	4.04648i	0.259227	+	0.149665i
$732$		0			0
$733$	12.5202	+	21.6857i	0.462445	+	0.800979i	0.999082	−	0.0428345i	$-0.0136388\pi$
$733$	12.5202	+	21.6857i	0.462445	+	0.800979i	−0.536637	+	0.843813i	$0.680305\pi$
$734$		0			0
$735$	−5.17611	−	3.87065i	−0.190924	−	0.142771i
$736$		0			0
$737$	47.9478	−	27.6827i	1.76618	−	1.01971i
$738$		0			0
$739$	−45.0173	−	25.9908i	−1.65599	−	0.956086i	−0.974538	−	0.224224i	$-0.928015\pi$
$739$	−45.0173	−	25.9908i	−1.65599	−	0.956086i	−0.681452	−	0.731863i	$-0.738651\pi$
$740$		0			0
$741$	−13.4878	+	8.39588i	−0.495486	+	0.308430i
$742$		0			0
$743$			26.4603i			0.970735i	0.874310	+	0.485367i	$0.161314\pi$
$743$			26.4603i			0.970735i	−0.874310	+	0.485367i	$0.838686\pi$
$744$		0			0
$745$	9.94549	+	5.74203i	0.364375	+	0.210372i
$746$		0			0
$747$	0.768946	+	11.5682i	0.0281343	+	0.423260i
$748$		0			0
$749$	18.4916	−	15.8800i	0.675670	−	0.580242i
$750$		0			0
$751$	9.69510	+	16.7924i	0.353779	+	0.612763i	0.986908	−	0.161283i	$-0.0515631\pi$
$751$	9.69510	+	16.7924i	0.353779	+	0.612763i	−0.633129	+	0.774046i	$0.718230\pi$
$752$		0			0
$753$	14.2323	−	0.472491i	0.518652	−	0.0172185i
$754$		0			0
$755$			1.50081i			0.0546202i
$756$		0			0
$757$			5.19772i			0.188914i	0.995529	+	0.0944572i	$0.0301115\pi$
$757$			5.19772i			0.188914i	−0.995529	+	0.0944572i	$0.969888\pi$
$758$		0			0
$759$	0.945403	−	0.0313861i	0.0343160	−	0.00113924i
$760$		0			0
$761$	−18.8681	−	32.6805i	−0.683969	−	1.18467i	−0.973760	−	0.227578i	$-0.926919\pi$
$761$	−18.8681	−	32.6805i	−0.683969	−	1.18467i	0.289791	−	0.957090i	$-0.406414\pi$
$762$		0			0
$763$	−4.29288	+	12.2277i	−0.155413	+	0.442671i
$764$		0			0
$765$	0.458511	+	6.89796i	0.0165775	+	0.249396i
$766$		0			0
$767$	28.4559	+	16.4290i	1.02748	+	0.593218i
$768$		0			0
$769$		−	13.9517i		−	0.503110i	−0.967843	−	0.251555i	$-0.919058\pi$
$769$		−	13.9517i		−	0.503110i	0.967843	−	0.251555i	$-0.0809419\pi$
$770$		0			0
$771$	19.7471	−	12.2921i	0.711173	−	0.442691i
$772$		0			0
$773$	−21.5519	−	12.4430i	−0.775169	−	0.447544i	0.0595465	−	0.998226i	$-0.481035\pi$
$773$	−21.5519	−	12.4430i	−0.775169	−	0.447544i	−0.834715	+	0.550682i	$0.814368\pi$
$774$		0			0
$775$	−9.13305	+	5.27297i	−0.328069	+	0.189411i
$776$		0			0
$777$	−27.3726	+	25.1320i	−0.981988	+	0.901604i
$778$		0			0
$779$	−2.40324	−	4.16254i	−0.0861051	−	0.149138i
$780$		0			0
$781$	−24.5878	−	14.1958i	−0.879822	−	0.507966i
$782$		0			0
$783$	−4.00028	−	40.0471i	−0.142958	−	1.43117i
$784$		0			0
$785$			3.77877i			0.134870i
$786$		0			0
$787$	4.90837	−	8.50154i	0.174964	−	0.303047i	−0.765185	−	0.643811i	$-0.777352\pi$
$787$	4.90837	−	8.50154i	0.174964	−	0.303047i	0.940149	+	0.340764i	$0.110686\pi$
$788$		0			0
$789$	12.2848	−	23.0087i	0.437350	−	0.819133i
$790$		0			0
$791$	10.0785	−	1.89613i	0.358350	−	0.0674188i
$792$		0			0
$793$	−5.35587	−	9.27663i	−0.190192	−	0.329423i
$794$		0			0
$795$	4.23181	−	0.140490i	0.150087	−	0.00498268i
$796$		0			0
$797$		−	11.3322i		−	0.401406i	−0.979652	−	0.200703i	$-0.935677\pi$
$797$		−	11.3322i		−	0.401406i	0.979652	−	0.200703i	$-0.0643226\pi$
$798$		0			0
$799$	−25.2002			−0.891518
$800$		0			0
$801$	27.4840	+	41.0507i	0.971100	+	1.45045i
$802$		0			0
$803$	38.2222	−	22.0676i	1.34883	−	0.778748i
$804$		0			0
$805$	−0.158870	−	0.0557758i	−0.00559942	−	0.00196584i
$806$		0			0
$807$	−10.8341	+	20.2917i	−0.381378	+	0.714301i
$808$		0			0
$809$	−19.0031	−	10.9714i	−0.668113	−	0.385735i	0.127248	−	0.991871i	$-0.459385\pi$
$809$	−19.0031	−	10.9714i	−0.668113	−	0.385735i	−0.795361	+	0.606136i	$0.792719\pi$
$810$		0			0
$811$	12.2220			0.429171			0.214586	−	0.976705i	$-0.431160\pi$
$811$	12.2220			0.429171			0.214586	+	0.976705i	$0.431160\pi$
$812$		0			0
$813$	−17.2230	−	27.6683i	−0.604036	−	0.970370i
$814$		0			0
$815$	−1.73664	+	3.00796i	−0.0608320	+	0.105364i
$816$		0			0
$817$	−2.98680	+	1.72443i	−0.104495	+	0.0603302i
$818$		0			0
$819$	9.86718	+	38.2699i	0.344787	+	1.33726i
$820$		0			0
$821$	−22.2720	−	38.5763i	−0.777299	−	1.34632i	−0.933493	−	0.358595i	$-0.883256\pi$
$821$	−22.2720	−	38.5763i	−0.777299	−	1.34632i	0.156195	−	0.987726i	$-0.450077\pi$
$822$		0			0
$823$	−13.6219	+	23.5938i	−0.474830	+	0.822429i	−0.999584	−	0.0288241i	$-0.990824\pi$
$823$	−13.6219	+	23.5938i	−0.474830	+	0.822429i	0.524755	+	0.851254i	$0.324157\pi$
$824$		0			0
$825$	−31.7222	+	19.7464i	−1.10443	+	0.687483i
$826$		0			0
$827$	−10.2913			−0.357864			−0.178932	−	0.983861i	$-0.557264\pi$
$827$	−10.2913			−0.357864			−0.178932	+	0.983861i	$0.557264\pi$
$828$		0			0
$829$	−16.2859	+	28.2081i	−0.565634	+	0.979707i	0.431356	+	0.902182i	$0.358035\pi$
$829$	−16.2859	+	28.2081i	−0.565634	+	0.979707i	−0.996990	+	0.0775252i	$0.975298\pi$
$830$		0			0
$831$	−18.9662	+	35.5226i	−0.657929	+	1.23227i
$832$		0			0
$833$	−4.57197	+	29.9120i	−0.158409	+	1.03639i
$834$		0			0
$835$	7.96232	−	4.59705i	0.275547	−	0.159087i
$836$		0			0
$837$	4.78103	−	10.5909i	0.165257	−	0.366077i
$838$		0			0
$839$	−4.55619			−0.157297			−0.0786486	−	0.996902i	$-0.525061\pi$
$839$	−4.55619			−0.157297			−0.0786486	+	0.996902i	$0.525061\pi$
$840$		0			0
$841$	30.9915			1.06867
$842$		0			0
$843$	−36.8266	+	1.22259i	−1.26838	+	0.0421084i
$844$		0			0
$845$	5.44432	−	3.14328i	0.187290	−	0.108132i
$846$		0			0
$847$	−19.9264	+	17.1122i	−0.684681	+	0.587981i
$848$		0			0
$849$	13.1763	+	7.03504i	0.452208	+	0.241442i
$850$		0			0
$851$	−0.484032	+	0.838369i	−0.0165924	+	0.0287389i
$852$		0			0
$853$	50.6930			1.73570			0.867848	−	0.496830i	$-0.165503\pi$
$853$	50.6930			1.73570			0.867848	+	0.496830i	$0.165503\pi$
$854$		0			0
$855$	−2.64347	−	1.30058i	−0.0904048	−	0.0444790i
$856$		0			0
$857$	3.66887	−	6.35467i	0.125326	−	0.217071i	−0.796534	−	0.604594i	$-0.793336\pi$
$857$	3.66887	−	6.35467i	0.125326	−	0.217071i	0.921860	+	0.387522i	$0.126669\pi$
$858$		0			0
$859$	28.8455	+	49.9619i	0.984195	+	1.70468i	0.645458	+	0.763795i	$0.276666\pi$
$859$	28.8455	+	49.9619i	0.984195	+	1.70468i	0.338737	+	0.940881i	$0.390000\pi$
$860$		0			0
$861$	−11.6706	+	2.59935i	−0.397733	+	0.0885856i
$862$		0			0
$863$	31.1345	−	17.9755i	1.05983	−	0.611894i	0.134445	−	0.990921i	$-0.457075\pi$
$863$	31.1345	−	17.9755i	1.05983	−	0.611894i	0.925385	+	0.379027i	$0.123741\pi$
$864$		0			0
$865$	−4.47467	+	7.75035i	−0.152143	+	0.263520i
$866$		0			0
$867$	2.47969	−	1.54356i	0.0842148	−	0.0524220i
$868$		0			0
$869$	0.209329			0.00710101
$870$		0			0
$871$	52.1883	+	30.1309i	1.76833	+	1.02095i
$872$		0			0
$873$	1.43027	+	21.5174i	0.0484073	+	0.728252i
$874$		0			0
$875$	13.4670	−	2.53363i	0.455267	−	0.0856523i
$876$		0			0
$877$	43.3964	−	25.0550i	1.46539	−	0.846046i	0.466142	−	0.884710i	$-0.345644\pi$
$877$	43.3964	−	25.0550i	1.46539	−	0.846046i	0.999252	+	0.0386646i	$0.0123104\pi$
$878$		0			0
$879$	39.3722	−	1.30710i	1.32799	−	0.0440875i
$880$		0			0
$881$	47.9585			1.61576			0.807882	−	0.589344i	$-0.200614\pi$
$881$	47.9585			1.61576			0.807882	+	0.589344i	$0.200614\pi$
$882$		0			0
$883$		−	0.345258i		−	0.0116188i	−0.999983	−	0.00580942i	$-0.998151\pi$
$883$		−	0.345258i		−	0.0116188i	0.999983	−	0.00580942i	$-0.00184921\pi$
$884$		0			0
$885$	0.202169	+	6.08969i	0.00679585	+	0.204703i
$886$		0			0
$887$	−13.7032	−	23.7346i	−0.460109	−	0.796931i	0.538857	−	0.842397i	$-0.318856\pi$
$887$	−13.7032	−	23.7346i	−0.460109	−	0.796931i	−0.998966	+	0.0454656i	$0.985523\pi$
$888$		0			0
$889$	4.00641	+	21.2952i	0.134371	+	0.714220i
$890$		0			0
$891$	15.6856	−	38.0669i	0.525487	−	1.27529i
$892$		0			0
$893$	5.36959	−	9.30041i	0.179687	−	0.311226i
$894$		0			0
$895$			2.14280i			0.0716258i
$896$		0			0
$897$	0.544092	+	0.874071i	0.0181667	+	0.0291844i
$898$		0			0
$899$	15.0004	+	8.66049i	0.500292	+	0.288844i
$900$		0			0
$901$	−9.91157	−	17.1673i	−0.330202	−	0.571927i
$902$		0			0
$903$	1.86515	+	8.37417i	0.0620682	+	0.278675i
$904$		0			0
$905$	6.86014	−	3.96070i	0.228039	−	0.131658i
$906$		0			0
$907$	7.67380	+	4.43047i	0.254804	+	0.147111i	0.621962	−	0.783047i	$-0.286336\pi$
$907$	7.67380	+	4.43047i	0.254804	+	0.147111i	−0.367158	+	0.930159i	$0.619669\pi$
$908$		0			0
$909$	10.3636	+	5.09885i	0.343737	+	0.169118i
$910$		0			0
$911$		−	17.2124i		−	0.570272i	−0.958487	−	0.285136i	$-0.907961\pi$
$911$		−	17.2124i		−	0.570272i	0.958487	−	0.285136i	$-0.0920388\pi$
$912$		0			0
$913$	−15.3106	−	8.83959i	−0.506707	−	0.292548i
$914$		0			0
$915$	0.935542	−	1.75222i	0.0309281	−	0.0579266i
$916$		0			0
$917$	36.9343	+	43.0086i	1.21968	+	1.42027i
$918$		0			0
$919$	−2.91012	−	5.04048i	−0.0959961	−	0.166270i	0.814028	−	0.580826i	$-0.197270\pi$
$919$	−2.91012	−	5.04048i	−0.0959961	−	0.166270i	−0.910024	+	0.414556i	$0.863937\pi$
$920$		0			0
$921$	1.31129	+	39.4982i	0.0432084	+	1.30151i
$922$		0			0
$923$		−	30.9025i		−	1.01717i
$924$		0			0
$925$		−	38.2407i		−	1.25734i
$926$		0			0
$927$	−13.2705	+	8.88482i	−0.435862	+	0.291816i
$928$		0			0
$929$	−3.36170	−	5.82263i	−0.110294	−	0.191034i	0.805595	−	0.592467i	$-0.201846\pi$
$929$	−3.36170	−	5.82263i	−0.110294	−	0.191034i	−0.915889	+	0.401432i	$0.868512\pi$
$930$		0			0
$931$	−10.0652	−	8.06092i	−0.329873	−	0.264186i
$932$		0			0
$933$	−36.6303	−	19.5576i	−1.19922	−	0.640287i
$934$		0			0
$935$	−9.12949	−	5.27091i	−0.298566	−	0.172377i
$936$		0			0
$937$			5.64519i			0.184420i	0.995740	+	0.0922102i	$0.0293932\pi$
$937$			5.64519i			0.184420i	−0.995740	+	0.0922102i	$0.970607\pi$
$938$		0			0
$939$	20.5485	+	33.0107i	0.670576	+	1.07726i
$940$		0			0
$941$	39.2739	+	22.6748i	1.28029	+	0.739177i	0.976902	−	0.213689i	$-0.0685479\pi$
$941$	39.2739	+	22.6748i	1.28029	+	0.739177i	0.303391	+	0.952866i	$0.401881\pi$
$942$		0			0
$943$	−0.269752	+	0.155741i	−0.00878433	+	0.00507164i
$944$		0			0
$945$	−5.05778	+	5.30362i	−0.164529	+	0.172527i
$946$		0			0
$947$	−0.0324938	−	0.0562810i	−0.00105591	−	0.00182889i	0.865497	−	0.500914i	$-0.167003\pi$
$947$	−0.0324938	−	0.0562810i	−0.00105591	−	0.00182889i	−0.866553	+	0.499085i	$0.833669\pi$
$948$		0			0
$949$	41.6025	+	24.0192i	1.35048	+	0.779697i
$950$		0			0
$951$	−3.11946	+	1.94180i	−0.101155	+	0.0629672i
$952$		0			0
$953$		−	33.3269i		−	1.07956i	−0.841805	−	0.539781i	$-0.818507\pi$
$953$		−	33.3269i		−	1.07956i	0.841805	−	0.539781i	$-0.181493\pi$
$954$		0			0
$955$	−5.26770	+	9.12393i	−0.170459	+	0.295243i
$956$		0			0
$957$	54.1379	+	28.9052i	1.75003	+	0.934372i
$958$		0			0
$959$	−3.96235	+	11.2862i	−0.127951	+	0.364450i
$960$		0			0
$961$	−12.9995	−	22.5158i	−0.419339	−	0.726316i
$962$		0			0
$963$	−15.3761	−	22.9660i	−0.495487	−	0.740070i
$964$		0			0
$965$			6.70862i			0.215958i
$966$		0			0
$967$	−8.68323			−0.279234			−0.139617	−	0.990206i	$-0.544587\pi$
$967$	−8.68323			−0.279234			−0.139617	+	0.990206i	$0.544587\pi$
$968$		0			0
$969$	0.457651	+	13.7852i	0.0147019	+	0.442846i
$970$		0			0
$971$	37.7352	−	21.7864i	1.21098	−	0.699159i	0.248007	−	0.968758i	$-0.420225\pi$
$971$	37.7352	−	21.7864i	1.21098	−	0.699159i	0.962973	+	0.269599i	$0.0868912\pi$
$972$		0			0
$973$	7.25453	+	38.5599i	0.232569	+	1.23617i
$974$		0			0
$975$	−35.8772	−	19.1555i	−1.14899	−	0.613466i
$976$		0			0
$977$	16.6770	+	9.62846i	0.533544	+	0.308042i	0.742458	−	0.669892i	$-0.233660\pi$
$977$	16.6770	+	9.62846i	0.533544	+	0.308042i	−0.208914	+	0.977934i	$0.566993\pi$
$978$		0			0
$979$	−75.3320			−2.40762
$980$		0			0
$981$	13.1851	+	6.48705i	0.420968	+	0.207116i
$982$		0			0
$983$	12.6512	−	21.9125i	0.403510	−	0.698900i	−0.590637	−	0.806938i	$-0.701123\pi$
$983$	12.6512	−	21.9125i	0.403510	−	0.698900i	0.994147	+	0.108037i	$0.0344567\pi$
$984$		0			0
$985$	−3.88630	+	2.24376i	−0.123828	+	0.0714920i
$986$		0			0
$987$	−18.0676	−	19.6784i	−0.575097	−	0.626371i
$988$		0			0
$989$	0.111751	+	0.193559i	0.00355348	+	0.00615481i
$990$		0			0
$991$	−6.86308	+	11.8872i	−0.218013	+	0.377609i	−0.954200	−	0.299168i	$-0.903291\pi$
$991$	−6.86308	+	11.8872i	−0.218013	+	0.377609i	0.736187	+	0.676778i	$0.236624\pi$
$992$		0			0
$993$	−1.32620	−	2.13051i	−0.0420857	−	0.0676098i
$994$		0			0
$995$	−7.63161			−0.241938
$996$		0			0
$997$	−1.12122	+	1.94201i	−0.0355094	+	0.0615041i	−0.883234	−	0.468933i	$-0.844639\pi$
$997$	−1.12122	+	1.94201i	−0.0355094	+	0.0615041i	0.847725	+	0.530437i	$0.177972\pi$
$998$		0			0
$999$	24.5905	+	34.2158i	0.778008	+	1.08254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.13		48
3.2	odd	2	inner	672.2.bi.c.17.4		48
4.3	odd	2		168.2.ba.c.101.19	yes	48
7.5	odd	6	inner	672.2.bi.c.593.21		48
8.3	odd	2		168.2.ba.c.101.22	yes	48
8.5	even	2	inner	672.2.bi.c.17.12		48
12.11	even	2		168.2.ba.c.101.6	yes	48
21.5	even	6	inner	672.2.bi.c.593.12		48
24.5	odd	2	inner	672.2.bi.c.17.21		48
24.11	even	2		168.2.ba.c.101.3	yes	48
28.19	even	6		168.2.ba.c.5.3	✓	48
56.5	odd	6	inner	672.2.bi.c.593.4		48
56.19	even	6		168.2.ba.c.5.6	yes	48
84.47	odd	6		168.2.ba.c.5.22	yes	48
168.5	even	6	inner	672.2.bi.c.593.13		48
168.131	odd	6		168.2.ba.c.5.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.3	✓	48	28.19	even	6
168.2.ba.c.5.6	yes	48	56.19	even	6
168.2.ba.c.5.19	yes	48	168.131	odd	6
168.2.ba.c.5.22	yes	48	84.47	odd	6
168.2.ba.c.101.3	yes	48	24.11	even	2
168.2.ba.c.101.6	yes	48	12.11	even	2
168.2.ba.c.101.19	yes	48	4.3	odd	2
168.2.ba.c.101.22	yes	48	8.3	odd	2
672.2.bi.c.17.4		48	3.2	odd	2	inner
672.2.bi.c.17.12		48	8.5	even	2	inner
672.2.bi.c.17.13		48	1.1	even	1	trivial
672.2.bi.c.17.21		48	24.5	odd	2	inner
672.2.bi.c.593.4		48	56.5	odd	6	inner
672.2.bi.c.593.12		48	21.5	even	6	inner
672.2.bi.c.593.13		48	168.5	even	6	inner
672.2.bi.c.593.21		48	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0574700 + 1.73110i) q^{3} +(0.461663 - 0.266541i) q^{5} +(-0.489180 - 2.60014i) q^{7} +(-2.99339 + 0.198972i) q^{9} +O(q^{10})\)	\(q+(0.0574700 + 1.73110i) q^{3} +(0.461663 - 0.266541i) q^{5} +(-0.489180 - 2.60014i) q^{7} +(-2.99339 + 0.198972i) q^{9} +(2.28733 - 3.96177i) q^{11} +4.97924 q^{13} +(0.487941 + 0.783866i) q^{15} +(2.16139 - 3.74363i) q^{17} +(0.921087 + 1.59537i) q^{19} +(4.47297 - 0.996248i) q^{21} +(0.103387 - 0.0596907i) q^{23} +(-2.35791 + 4.08402i) q^{25} +(-0.516471 - 5.17042i) q^{27} +7.74542 q^{29} +(1.93668 + 1.11814i) q^{31} +(6.98966 + 3.73191i) q^{33} +(-0.918880 - 1.07000i) q^{35} +(-7.02261 + 4.05451i) q^{37} +(0.286157 + 8.61955i) q^{39} -2.60914 q^{41} +1.87217i q^{43} +(-1.32891 + 0.889722i) q^{45} +(-2.91482 - 5.04861i) q^{47} +(-6.52141 + 2.54387i) q^{49} +(6.60480 + 3.52642i) q^{51} +(2.29287 - 3.97137i) q^{53} -2.43867i q^{55} +(-2.70880 + 1.68618i) q^{57} +(5.71492 + 3.29951i) q^{59} +(-1.07564 - 1.86306i) q^{61} +(1.98166 + 7.68590i) q^{63} +(2.29873 - 1.32717i) q^{65} +(10.4812 + 6.05131i) q^{67} +(0.109272 + 0.175543i) q^{69} -6.20627i q^{71} +(8.35520 + 4.82388i) q^{73} +(-7.20535 - 3.84706i) q^{75} +(-11.4201 - 4.00935i) q^{77} +(0.0228792 + 0.0396280i) q^{79} +(8.92082 - 1.19121i) q^{81} -3.86459i q^{83} -2.30440i q^{85} +(0.445129 + 13.4081i) q^{87} +(-8.23362 - 14.2610i) q^{89} +(-2.43575 - 12.9467i) q^{91} +(-1.82431 + 3.41684i) q^{93} +(0.850463 + 0.491015i) q^{95} -7.18828i q^{97} +(-6.05860 + 12.3143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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